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Cosmic-ray cascades in the atmosphere

This article discusses the phenomenon of cosmic-ray cascades in the atmosphere, exploring topics such as inclusive fluxes, composition around the knee, and the transition to extra-galactic cosmic rays. It also covers the energetics of the extra-galactic component and provides examples from IceTop/IceCube. The article explains the boundary conditions and scaling for air showers, and the cascade equation for primary particles of mass A and energy E0. It also discusses the atmosphere, pressure, density, and interaction versus decay processes. The article explores various models, formulas, and simulations related to cascades in the atmosphere and provides insights into air shower arrays, spectrometers, and calorimeters. Additionally, it addresses current questions and challenges in the field of cosmic-ray research.

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Cosmic-ray cascades in the atmosphere

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  1. Cosmic-ray cascades in the atmosphere Air shower phenomenology Inclusive fluxes in the atmosphere Tom Gaisser CORSIKA summer school

  2. 1) Air showers • Generalities • Current questions • Composition around the knee • Transition to extra-galactic cosmic rays? • Energetics of extra-galactic component • Example of IceTop/IceCube Tom Gaisser CORSIKA summer school

  3. Cascades in the atmosphere Tom Gaisser CORSIKA summer school

  4. Boundary conditions & scaling • Air shower, primary of mass A, energy E0 : • N(X=0) = A d (E- E0 /A) for nucleons • N(X=0) = 0 for all other particles • Uncorrelated flux from power-law spectrum: • N(X=0) = fp(E) = K E-(g+1) • ~ 1.7 E-2.7 ( cm-2 s-1 sr-1 GeV-1 ), top of atmosphere • Fji( Ei,Ej) has no explicit dimension, F  F(x) • x = Ei/Ej &∫…F(Ei,Ej) dEj / Ei  ∫…F(x) dx / x2 • Small scaling violations from mi, LQCD ~ GeV Tom Gaisser CORSIKA summer school

  5. The atmosphere The atmosphere (exponential approximation) Pressure = Xv = Xo exp{ -hv / ho } , where ho = 6.4 km for Xv < 200 g / cm2 and X0 = 1030 g / cm2 Density = r = -dXv / dhv = Xv / ho Tom Gaisser CORSIKA summer school

  6. Cascade equation for p+/- Tom Gaisser CORSIKA summer school

  7. Relative magnitude of li and di = X cosq ( E / ei ) determines competition between interaction and decay Xv = 100 g / cm2 at 15 km altitude which is comparable to interaction lengths of hadrons in air Interaction vs. decay Tom Gaisser CORSIKA summer school

  8. Heitler’s pedagogical toy model of multiplicative cascades Tom Gaisser CORSIKA summer school

  9. p+/- m + n Warning: numerical values not correct Tom Gaisser CORSIKA summer school

  10. Modified NKG formula (Akeno) for hadronic cascades e+/- m+/- Greisen’s empical form for lateral distribution of low-energy ( few GeV) muons in EAS Lateral distributions Tom Gaisser CORSIKA summer school

  11. Super-simple simulations-- a useful guide for setting real simulations? • Use longitudinal development formula with starting point fluctuations. • : • Use NKG, Greisen lateral distributions • Map out response functions • Primary energy • Space and angular distributions • Example later (IceTop) Tom Gaisser CORSIKA summer school

  12. Spectrometers (DA = 1 resolution, good E resolution) Air showers Calorimeters (less good resolution) Air-shower arrays on the ground to overcome low flux. Don’t see primaries directly. Primary spectrum Knee Ankle Current questions Tom Gaisser CORSIKA summer school

  13. Aspen, April 26-30 B E-G A Tom Gaisser CORSIKA summer school

  14. 30 Rigidity-dependence • Acceleration, propagation • depend on B: rgyro = R/B • Rigidity, R = E/Ze • Ec(Z) ~ Z Rc • rSNR ~ parsec •  Emax ~ Z * 1015 eV • 1 < Z < 30 (p to Fe) • Slope change should occur within factor of 30 in energy • With characteristic pattern of increasing A • Problem: continuation of smooth spectrum to EeV Tom Gaisser CORSIKA summer school

  15. B. Peters, Nuovo Cimento 22 (1961) 800 B. Peters on the knee and ankle <A> should begin to decrease again for E > 30 x Eknee Peters cycle: systematic increase of < A > approaching Emax Tom Gaisser CORSIKA summer school

  16. M. Roth et al., Proc ICRC 2003 (Tsukuba) vol 1, p 139 Recent KASCADE data show increasing fraction of heavy nuclei with expected cutoff sequence starting at ~3 PeV • Based on Nm/Ne analysis (KASCADE talks on Saturday) • KASCADE Grande to extend to > 1017 eV 1015 1016 1017 Tom Gaisser CORSIKA summer school

  17. piering Three new kilometer-scale detectors Tom Gaisser CORSIKA summer school

  18. Sketch of ground array with fluorescence detector – Auger Project realizes this concept Hi-Res stereo fluorescence detector in Utah AGASA (Akeno, Japan) 100 km2 ground array Air shower detectors Tom Gaisser CORSIKA summer school

  19. Measuring the energy of UHECR • Ground array samples shower front • Well-defined acceptance • Simulation relates observed ground parameter to energy • m / e for composition • Fluorescence technique tracks shower profile • Track-length integral gives calorimetric measure of energy: E ~ a∫ N(X) dX • Xmax sensitive to primary mass: Xmax ~ Lln(E0/A) Tom Gaisser CORSIKA summer school

  20. HR2 Profile Plot(from Doug Bergman’s HiRes talk at Aspen, Jan 2002) • Top plot shows observed NPE (points) together with predicted NPE from final GH fit: green-fluorescence, blue-Cerenkov, red-total • Bottom plot shows shower size initially (blue) and after Cerenkov correction (black) along with GH fit • Note: need to correct for lost energy (n, high energy mand e-m shower into the ground) Tom Gaisser CORSIKA summer school

  21. AGASA 2 x 1020 eV event All charged particles m N. Hayashida et al., PRL 73 (1994) 3491 Tom Gaisser CORSIKA summer school

  22. Biggest event Fly’s Eye, Ap. J. 441 (1995) 295 • Comparison to • Proton showers • Iron showers • g showers • Horizontal EAS • only muons survive • Haverah Park: g/p<40%, E>1019eV • AGASA: similar limit • Limit on g showers constrains TD models Tom Gaisser CORSIKA summer school

  23. Xmax vs Energy • Protons penetrate deeper into atmosphere • Heavy nuclei develop higher up • Plot shows a summary of data over 5 decades • Several techniques Tom Gaisser CORSIKA summer school

  24. HiRes new composition result: transition occurs before ankle Original Fly’s Eye (1993): transition coincides with ankle 0.3 EeV 3 EeV G. Archbold, P. Sokolsky, et al., Proc. 28th ICRC, Tsukuba, 2003 Where is transition to extragalactic CR? Stereo Tom Gaisser CORSIKA summer school

  25. Energy content of extra-galactic component depends on location of transition • Composition signature: • transition back to protons • Uncertainties: • Normalization point: • 1018 to 1019.5 used • Factor 10 / decade • Spectral slope • a=2.3 for rel. shock • =2.0 non-rel. • Emin ~ mp (gshock)2 Tom Gaisser CORSIKA summer school

  26. Power needed for extragalactic cosmic rays assuming transition at 1019 eV • Energy density in UHECR, CR ~ 2 x 10-19 erg/cm3 • Such an estimate requires extrapolation of UHECR to low energy • CR = (4/c)  E(E) dE = (4/c){E2(E)}E=1019eV x ln{Emax/Emin} • This gives CR ~ 2 x 10-19 erg/cm3 for differential index  = 2, (E) ~ E-2 • Power required ~ CR/1010 yr ~ 1.3 x 1037 erg/Mpc3/s • Estimates depend on cosmology and extragalactic magnetic fields: • 3 x 10-3 galaxies/Mpc3 5 x 1039 erg/s/Galaxy • 3 x 10-6 clusters/Mpc3 4 x 1042 erg/s/Galaxy Cluster • 10-7 AGN/Mpc3 1044 erg/s/AGN • ~1000 GRB/yr 3 x 1052 erg/GRB Tom Gaisser CORSIKA summer school

  27. IceCube with IceTop after 04/05 deployment season 4 IceTop Stations deployed in December 2004 1st IceCube string deployed on Jan 29 2005 Tom Gaisser CORSIKA summer school

  28. IceTop • Calibration • pointing • Dq/q • E deposition • Tag background • Reconstruction • rejection • Cosmic-rays • 3 x 1014 – 1018 eV • ‘knee’ to ‘ankle’ = galactic to extragalactic? Tom Gaisser CORSIKA summer school

  29. ~ 5-10 TeV IceTop station • Two Ice Tanks 2.7 m2 x 0.9 m deep (scaled-down version of Haverah, Auger) • Integrated with IceCube: same hardware, software • Coincidence between tanks = potential air shower • Local coincidence with no hit at neighboring station tags muon in deep detector • Signal in single tank = potential muon • Significant area for horizontal muons • Low Gain/High Gain operation to achieve dynamic range • Two DOMs/tank gives redundancy against failure of any single DOM because only 1 low-gain detector is needed per station Tom Gaisser CORSIKA summer school

  30. Run 872 Event 5945 Tom Gaisser CORSIKA summer school

  31. Simulations of R Engel (Aspen) comparing KASCADE-Grande with IceCube/IceTop Tom Gaisser CORSIKA summer school

  32. IceTop and SPASE 2 Tom Gaisser CORSIKA summer school

  33. IceTop SPASE Coincidence IceTop/SPASE coincidence rate 0.06 Hz Coincidence within +/- 200 msec signal and flat background Coincidence within +/- 3 msec - 1.4 msec offset Tom Gaisser CORSIKA summer school

  34. Simulated response of single station hits (mostly single muons in deep ice) Low coincidence rate is due to 4-string geometry, dq < 6o in ‘05 Tom Gaisser CORSIKA summer school

  35. Core location distributions, Ep =18 TeV Tom Gaisser CORSIKA summer school

  36. Core locations for Ep = 2.7 PeV Note that ring of distant singles from PeV showers will be removed by surrounding stations in larger array Tom Gaisser CORSIKA summer school

  37. Ep, cos(q) distributions of 4-folds 3-fold rate ~ 0.30 Hz Tom Gaisser CORSIKA summer school

  38. Azimuthal distributions 0o 90o Tom Gaisser CORSIKA summer school

  39. (VEM*factor) Spectrum of deposited energy for 4-fold events Tom Gaisser CORSIKA summer school

  40. Comparison of simulated vs measured rates Measured rate: f3 + f4 = 0.73 Hz Coincidence rate with string 21 trigger ~ .07 Hz Tom Gaisser CORSIKA summer school

  41. IceTop daily monitoring pagehttp://icecube.bartol.udel.edu IceTop trigger: > 10 DOMs > threshold in 2 ms Hard local coincidence between DOMs in adjacent tanks Tom Gaisser CORSIKA summer school

  42. Angular distributions IceTop Triggers In-Ice Triggers Tom Gaisser CORSIKA summer school

  43. IceTop display (ATWD ch 1) Event 79 Voltage vs time (20 ns per division) Low-gain DOMs High-gain DOMs 0.8 v 39 100 200 ns 30 29 21 Tom Gaisser CORSIKA summer school

  44. Goal: express wave-forms in units of VEM (Vertical Equivalent Muon ) as in Auger Auger Compress by ~10 for IceTop Tom Gaisser CORSIKA summer school

  45. Wave forms IceTop Spacing 125 m Width ~ 100 ns Auger: Spacing 1500 m Widths ~ 1 msec Tom Gaisser CORSIKA summer school

  46. Expected signals in 2006 • Single station rate ~ 120 Hz • ~ 1.5 Hz coincident rate for calibration • Cosmic-ray showers 3.1014 -1017 eV • Total rate of > 4-fold EAS: ~ 4 Hz • ~100 / day > 1016 eV (~50 m @ 2 km) • ~ 1 / day > 1017 eV (~300 m @ 2 km) • ~ 10% of IceTop triggers give coincidences with deep array Tom Gaisser CORSIKA summer school

  47. DOMs in IceTop Tom Gaisser CORSIKA summer school

  48. Fill tanks Most tanks to be filled with water from drill system --How to filter and remove contaminants is TBD Tom Gaisser CORSIKA summer school

  49. Daan Hubert 8-dec-04? Steffen-CRW_0361 19-jan-05 JohnKelley 02-jan-05 Station 39 Tom Gaisser CORSIKA summer school

  50. John Kelley P105008 06-jan-05 John Kelley P105005 06-jan-05 Steffen CRW_0344 19-jan-05 Steffen CRW_0332 19-jan-05 Station 29, TANK 102 (only tank with bubbles) Tom Gaisser CORSIKA summer school

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